Efficient numerical procedures for solving closed-loop Stackelberg strategies with small singular perturbation parameter

In this paper, the computation of the linear closed-loop Stackelberg strategies with small singular perturbation parameter that characterizes singularly perturbed systems (SPS) are studied. The attention is focused on a new numerical algorithm for solving a set of cross-coupled algebraic Lyapunov and Riccati equations (CALRE). It is proven that the new algorithm guarantees the local quadratic convergence. A numerical example is solved to show a reduction of the average CPU time compared with the existing algorithm. keywords: Stackelberg strategies, cross-coupled algebraic Lyapunov and Riccati equations, singularly perturbed systems, Newton’s method.